Definitions [3]
Closed Curves: Figures in which initial and endpoints coincide with each other are called closed figures.
Region: The interior of a curve together with its boundary is called its region.
Open Curves: A curve has two endpoints, and when it does not enclose the area within itself it is known as an open curve.
Simple Curves: Simple curve are those curves which changes direction but does not cross itself while changing direction.
Non-simple curve: If a curve does cross itself, then it is called a Non-simple curve.
A polygon is any closed, flat shape that is formed by straight line segments (sides).
Example:
A polygon is a closed, flat figure made up of straight-line segments. A polygon is called a regular polygon if it is both:
-
Equiangular: All its interior angles are equal.
-
Equilateral: All its sides are equal in length.
Formulae [6]
Sum of interior angles of a polygon = (n – 2) × 180°
Explanation:
- A polygon with n sides can be divided into smaller triangles by drawing diagonals from one vertex.
- Each triangle has a total angle sum of 180°.
- Since the number of triangles formed inside the polygon is (n – 2).
- The total sum of all interior angles is therefore (n – 2) × 180°.
Each exterior angle = `"360°"/"n"`
Sum of interior angles = (n − 2) × 180∘
Each interior angle = `"(n − 2) × 180° " /"n"`
Number of sides (n) of a regular polygon = `"360°"/"exterior angle "`
Relationship between interior and exterior angles = Exterior angle + Interior angle = 180°
